In subarray structures, each antenna is connected to only one RF chain through a PS. Therefore, the total number of PS is reduced to \(N_{\sf {T}}\)  (instead of \(N_{\sf {T}}\times N_{\sf {RF}}\) ). These structures can either have fixed connections, as shown in Fig. REF (b), or dynamic connections (Fig. REF (c)), where the connections between antennas and RF chains can be switched dynamically using a multiplexers network. It is shown in [1]} that such dynamic structure improves the spectral efficiency of the system by providing more degrees of freedom in HBF design compared to FSA-HBF, while reducing the power consumption compared to FC-HBF. The AP in both subarray structures consists of two parts, i) PS and ii) connections between RF chains and PS. Therefore, the general feasible AP matrix for subarray beamforming can be written as
\(\mathbf {A}_{\text{q}} =\underbrace{\text{diag}\big (a_{1}, ..., a_{N_{\sf {T}}} \big )}_{\text{Phase-shifters}} \mathbf {S},\) 
